An adaptive isogeometric analysis collocation method with a recovery-based error estimator

Yue Jia; Cosmin Anitescu; Yongjie Jessica Zhang; Timon Rabczuk

doi:10.1016/j.cma.2018.10.039

An adaptive isogeometric analysis collocation method with a recovery-based error estimator

Yue Jia, Cosmin Anitescu, Yongjie Jessica Zhang, Timon Rabczuk

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

In this paper, we propose an enhanced isogeometric analysis (IGA) collocation method. It is well known that the location of the collocation points plays an important role in the accuracy and stability of IGA collocation methods. This is particularly true for non-uniform meshes and domains generated from multi-patch geometries. We present an enhanced collocation method based on Gauss points, which has improved accuracy as compared to using C¹ splines and a recovery-based error estimator that can be derived by sampling the solution at particular points in the domain. Adaptivity is implemented using a hierarchical spline basis, which satisfies the C1 continuity requirement. The proposed approach has been tested by several benchmark problems, including multipatch domains and geometries with re-entrant corners.

Original language	English
Pages (from-to)	52-74
Number of pages	23
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	345
DOIs	https://doi.org/10.1016/j.cma.2018.10.039
Publication status	Published - 2019 Mar 1
Externally published	Yes

Bibliographical note

Funding Information:
Y. Jia was partially supported by the China Scholarship Council (CSC) , the top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University , China, and the Fundamental Research Funds for the Central Universities , China (Nos. 3102017jc01003 , 3102017jc11001 ). Y. Zhang was supported in part by the PECASE award N00014-16-1-2254 (USA), NSF CAREER Award OCI-1149591 (USA) and NSF , USA grant CBET-1804929 . C. Anitescu and T. Rabczuk acknowledge the partial support of the European Union (European Research Council project number 615132 ) and of the German Research Foundation (DFG project number 392023639 ).

Funding Information:
Y. Jia was partially supported by the China Scholarship Council (CSC), the top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University, China, and the Fundamental Research Funds for the Central Universities, China (Nos. 3102017jc01003, 3102017jc11001). Y. Zhang was supported in part by the PECASE awardN00014-16-1-2254 (USA), NSF CAREER AwardOCI-1149591 (USA) and NSF, USA grant CBET-1804929. C. Anitescu and T. Rabczuk acknowledge the partial support of the European Union (European Research Council project number 615132) and of the German Research Foundation (DFG project number 392023639).

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

Error estimation
Gaussian-collocation points
IGA collocation method
Linear elasticity
PHT-spline

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

Access to Document

10.1016/j.cma.2018.10.039

Cite this

@article{d837191a5ad249169b9f4e0966571585,

title = "An adaptive isogeometric analysis collocation method with a recovery-based error estimator",

abstract = "In this paper, we propose an enhanced isogeometric analysis (IGA) collocation method. It is well known that the location of the collocation points plays an important role in the accuracy and stability of IGA collocation methods. This is particularly true for non-uniform meshes and domains generated from multi-patch geometries. We present an enhanced collocation method based on Gauss points, which has improved accuracy as compared to using C1 splines and a recovery-based error estimator that can be derived by sampling the solution at particular points in the domain. Adaptivity is implemented using a hierarchical spline basis, which satisfies the C1 continuity requirement. The proposed approach has been tested by several benchmark problems, including multipatch domains and geometries with re-entrant corners.",

keywords = "Error estimation, Gaussian-collocation points, IGA collocation method, Linear elasticity, PHT-spline",

author = "Yue Jia and Cosmin Anitescu and Zhang, {Yongjie Jessica} and Timon Rabczuk",

note = "Funding Information: Y. Jia was partially supported by the China Scholarship Council (CSC) , the top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University , China, and the Fundamental Research Funds for the Central Universities , China (Nos. 3102017jc01003 , 3102017jc11001 ). Y. Zhang was supported in part by the PECASE award N00014-16-1-2254 (USA), NSF CAREER Award OCI-1149591 (USA) and NSF , USA grant CBET-1804929 . C. Anitescu and T. Rabczuk acknowledge the partial support of the European Union (European Research Council project number 615132 ) and of the German Research Foundation (DFG project number 392023639 ). Funding Information: Y. Jia was partially supported by the China Scholarship Council (CSC), the top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University, China, and the Fundamental Research Funds for the Central Universities, China (Nos. 3102017jc01003, 3102017jc11001). Y. Zhang was supported in part by the PECASE awardN00014-16-1-2254 (USA), NSF CAREER AwardOCI-1149591 (USA) and NSF, USA grant CBET-1804929. C. Anitescu and T. Rabczuk acknowledge the partial support of the European Union (European Research Council project number 615132) and of the German Research Foundation (DFG project number 392023639). Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2019",

month = mar,

day = "1",

doi = "10.1016/j.cma.2018.10.039",

language = "English",

volume = "345",

pages = "52--74",

journal = "Computer Methods in Applied Mechanics and Engineering",

issn = "0045-7825",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - An adaptive isogeometric analysis collocation method with a recovery-based error estimator

AU - Jia, Yue

AU - Anitescu, Cosmin

AU - Zhang, Yongjie Jessica

AU - Rabczuk, Timon

N1 - Funding Information: Y. Jia was partially supported by the China Scholarship Council (CSC) , the top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University , China, and the Fundamental Research Funds for the Central Universities , China (Nos. 3102017jc01003 , 3102017jc11001 ). Y. Zhang was supported in part by the PECASE award N00014-16-1-2254 (USA), NSF CAREER Award OCI-1149591 (USA) and NSF , USA grant CBET-1804929 . C. Anitescu and T. Rabczuk acknowledge the partial support of the European Union (European Research Council project number 615132 ) and of the German Research Foundation (DFG project number 392023639 ). Funding Information: Y. Jia was partially supported by the China Scholarship Council (CSC), the top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University, China, and the Fundamental Research Funds for the Central Universities, China (Nos. 3102017jc01003, 3102017jc11001). Y. Zhang was supported in part by the PECASE awardN00014-16-1-2254 (USA), NSF CAREER AwardOCI-1149591 (USA) and NSF, USA grant CBET-1804929. C. Anitescu and T. Rabczuk acknowledge the partial support of the European Union (European Research Council project number 615132) and of the German Research Foundation (DFG project number 392023639). Publisher Copyright: © 2018 Elsevier B.V.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - In this paper, we propose an enhanced isogeometric analysis (IGA) collocation method. It is well known that the location of the collocation points plays an important role in the accuracy and stability of IGA collocation methods. This is particularly true for non-uniform meshes and domains generated from multi-patch geometries. We present an enhanced collocation method based on Gauss points, which has improved accuracy as compared to using C1 splines and a recovery-based error estimator that can be derived by sampling the solution at particular points in the domain. Adaptivity is implemented using a hierarchical spline basis, which satisfies the C1 continuity requirement. The proposed approach has been tested by several benchmark problems, including multipatch domains and geometries with re-entrant corners.

AB - In this paper, we propose an enhanced isogeometric analysis (IGA) collocation method. It is well known that the location of the collocation points plays an important role in the accuracy and stability of IGA collocation methods. This is particularly true for non-uniform meshes and domains generated from multi-patch geometries. We present an enhanced collocation method based on Gauss points, which has improved accuracy as compared to using C1 splines and a recovery-based error estimator that can be derived by sampling the solution at particular points in the domain. Adaptivity is implemented using a hierarchical spline basis, which satisfies the C1 continuity requirement. The proposed approach has been tested by several benchmark problems, including multipatch domains and geometries with re-entrant corners.

KW - Error estimation

KW - Gaussian-collocation points

KW - IGA collocation method

KW - Linear elasticity

KW - PHT-spline

UR - http://www.scopus.com/inward/record.url?scp=85056777448&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2018.10.039

DO - 10.1016/j.cma.2018.10.039

M3 - Article

AN - SCOPUS:85056777448

SN - 0045-7825

VL - 345

SP - 52

EP - 74

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

An adaptive isogeometric analysis collocation method with a recovery-based error estimator

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this